71edo: Difference between revisions
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71edo is the 20th [[prime EDO]]. | 71edo is the 20th [[prime EDO]]. | ||
71edo is, quite unusually for an EDO this large, a [[dual-fifth]] system, with the flat fifth (which is near [[26edo]]'s fifth) supporting [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] and [[archy]]. | 71edo is, quite unusually for an EDO this large, a [[dual-fifth]] system, with the flat fifth (which is near [[26edo]]'s fifth) supporting [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] and [[archy]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2. | ||
== Theory == | == Theory == | ||
Revision as of 08:15, 3 April 2023
| ← 70edo | 71edo | 72edo → |
The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each.
71edo is the 20th prime EDO.
71edo is, quite unusually for an EDO this large, a dual-fifth system, with the flat fifth (which is near 26edo's fifth) supporting flattone temperament, and the sharp fifth (which is near 22edo's fifth) supporting superpyth and archy. Unlike small dual-fifth systems such as 18edo, both fifths are close approximations of 3/2.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.90 | +2.42 | -5.45 | -1.09 | +6.43 | +4.54 | -6.58 | -3.55 | +6.71 | +2.46 | -2.92 |
| Relative (%) | +46.8 | +14.3 | -32.2 | -6.5 | +38.0 | +26.9 | -38.9 | -21.0 | +39.7 | +14.5 | -17.3 | |
| Steps (reduced) |
113 (42) |
165 (23) |
199 (57) |
225 (12) |
246 (33) |
263 (50) |
277 (64) |
290 (6) |
302 (18) |
312 (28) |
321 (37) | |
It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&71 and 34&37 temperaments.
Intervals
| # | Cents | Diatonic interval category |
|---|---|---|
| 0 | 0.0 | perfect unison |
| 1 | 16.9 | superunison |
| 2 | 33.8 | superunison |
| 3 | 50.7 | subminor second |
| 4 | 67.6 | subminor second |
| 5 | 84.5 | minor second |
| 6 | 101.4 | minor second |
| 7 | 118.3 | minor second |
| 8 | 135.2 | supraminor second |
| 9 | 152.1 | neutral second |
| 10 | 169.0 | submajor second |
| 11 | 185.9 | major second |
| 12 | 202.8 | major second |
| 13 | 219.7 | major second |
| 14 | 236.6 | supermajor second |
| 15 | 253.5 | ultramajor second |
| 16 | 270.4 | subminor third |
| 17 | 287.3 | minor third |
| 18 | 304.2 | minor third |
| 19 | 321.1 | supraminor third |
| 20 | 338.0 | supraminor third |
| 21 | 354.9 | neutral third |
| 22 | 371.8 | submajor third |
| 23 | 388.7 | major third |
| 24 | 405.6 | major third |
| 25 | 422.5 | supermajor third |
| 26 | 439.4 | supermajor third |
| 27 | 456.3 | ultramajor third |
| 28 | 473.2 | subfourth |
| 29 | 490.1 | perfect fourth |
| 30 | 507.0 | perfect fourth |
| 31 | 523.9 | superfourth |
| 32 | 540.8 | superfourth |
| 33 | 557.7 | superfourth |
| 34 | 574.6 | low tritone |
| 35 | 591.5 | low tritone |
| 36 | 608.5 | high tritone |
| 37 | 625.4 | high tritone |
| 38 | 642.3 | subfifth |
| 39 | 659.2 | subfifth |
| 40 | 676.1 | subfifth |
| 41 | 693.0 | perfect fifth |
| 42 | 709.9 | perfect fifth |
| 43 | 726.8 | superfifth |
| 44 | 743.7 | ultrafifth |
| 45 | 760.6 | subminor sixth |
| 46 | 777.5 | subminor sixth |
| 47 | 794.4 | minor sixth |
| 48 | 811.3 | minor sixth |
| 49 | 828.2 | supraminor sixth |
| 50 | 845.1 | neutral sixth |
| 51 | 862.0 | submajor sixth |
| 52 | 878.9 | submajor sixth |
| 53 | 895.8 | major sixth |
| 54 | 912.7 | major sixth |
| 55 | 929.6 | supermajor sixth |
| 56 | 946.5 | ultramajor sixth |
| 57 | 963.4 | subminor seventh |
| 58 | 980.3 | minor seventh |
| 59 | 997.2 | minor seventh |
| 60 | 1014.1 | minor seventh |
| 61 | 1031.0 | supraminor seventh |
| 62 | 1047.9 | neutral seventh |
| 63 | 1064.8 | submajor seventh |
| 64 | 1081.7 | major seventh |
| 65 | 1098.6 | major seventh |
| 66 | 1115.5 | major seventh |
| 67 | 1132.4 | supermajor seventh |
| 68 | 1149.3 | ultramajor seventh |
| 69 | 1166.2 | suboctave |
| 70 | 1183.1 | suboctave |
| 71 | 1200.0 | perfect octave |